Question: Rewrite as a simplified fraction. ${2.\overline{13} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 213.1313...\\ 1x &= 2.1313...\end{align*}}$ Subtracting the two equations, we have: ${99x = 211}$ ${x = \dfrac{211}{99}} \text{or} {2 \dfrac{13}{99}}$